In a small saucepan add granulated sugar, brown sugar, water, cinnamon, cinnamon sticks, ginger, cloves, nutmeg, and pumpkin purèe. Stir together and bring to a simmer.
Turn the heat to low and simmer for 20 minutes. Remove from heat and strain through a fine mesh sieve or cheese cloth into an air tight container to cool completely.
For margarita:
Fill a cocktail shaker with ice. Add tequila, cointreau or orange liquor, lime juice and homemade pumpkin simple syrup.
Seal the top and shake the cocktail shaker until the outside is very cold. Strain into a low ball or margarita glass filled with fresh ice.
Garnish with a fresh lime wheel or dehydrated orange wheel.